A laboratory activity requires students to determine the force constant of an…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A laboratory activity requires students to determine the force constant of an unfamiliar spring. Five different brass washers are hung from the spring one at a time, and for each mass the average period of small vertical oscillations is measured. The timers used have a resolution of ±0.02s for a single-period measurement. The masses are known to ±1%.
Data collected:
Trial | Mass (kg) | Average period for 10 oscillations (s)
1 | 0.060 | 4.84
2 | 0.080 | 5.60
3 | 0.100 | 6.27
4 | 0.120 | 6.93
5 | 0.140 | 7.52
(Remember that each listed period corresponds to 10 oscillations.)
(a) For each trial, calculate the period of a single oscillation and then compute T2. Organize your results in a clear table.
(b) Describe the graph you would plot to obtain a straight line whose slope can be used to evaluate a property of the spring. Specify the quantity on each axis and state the expected mathematical form of the graph.
(c) Using the numerical data from part (a), determine the slope of the straight-line relationship and hence calculate the force constant of the spring.
(d) Estimate the percent uncertainty in the force constant that arises from the timing resolution and the stated mass uncertainties. Clearly state any assumptions you make in combining uncertainties.